Asgard's slightly higher North Peak was first ascended in 1953 by J. Weber, J. Marmet, and H. Röthlisberger, Swiss scientists on the Arctic Institute Baffin Island Expedition, led by the Canadian P. Baird.[3] Their route ascended the east side of the north peak, using a climbing traverse across snowfields and rock ribs, to reach the saddle between the two peaks, and thence to the top of the North Peak. The route is graded VI, 5.8/5.9 A1. It is still the most-traveled route and is the standard descent route for climbers making harder ascents on other faces.[4]

The South Peak was first climbed in 1971 by G. Lee, R. Wood, P. Clanky, J. Pavur, Y. Kamisawa and P. Koch. Since then, at least 13 routes have been put up on the two peaks, most involving highly technical free and aid climbing, with lengths varying from 800 m (2,600 ft) to 1,200 m (3,900 ft). One of the most notable routes was put up in 1975 by Charlie Porter as a solo climb. This was "the first Baffin modern, multi-day, technical, big-wall climb", with 40 pitches rated at Grade VII, 5.10, A4 and it was followed by "a 10-day walk-out to the fjord-head without food". The fact that this was all done solo was "a remarkable achievement".[4]